Solid and Spherical Geometry and Conic Sections: Being a Treatise on the Higher Branches of Synthetical Geometry, Containing the Solid and Spherical Geometry of Playfair ...William and Robert Chambers and sold by all booksellers, 1837 - 164 sider |
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Resultat 1-5 av 27
Side 5
... fore the angle ABF is equal to the angle ABC , and they are both in the same plane ; which is impossible : therefore the straight line BC is not above the plane in which are BD and BE . Wherefore the three straight lines BC , BD , BE ...
... fore the angle ABF is equal to the angle ABC , and they are both in the same plane ; which is impossible : therefore the straight line BC is not above the plane in which are BD and BE . Wherefore the three straight lines BC , BD , BE ...
Side 7
... fore AD is ( Pl . Ge . I. 33 ) both equal and parallel to BE ; for the same reason , CF is equal and parallel to BE ; there- fore AD and CF are each of them equal and parallel to BE . But straight lines that are parallel to the same ...
... fore AD is ( Pl . Ge . I. 33 ) both equal and parallel to BE ; for the same reason , CF is equal and parallel to BE ; there- fore AD and CF are each of them equal and parallel to BE . But straight lines that are parallel to the same ...
Side 9
... fore the planes CD , EF , though produced , do not meet one another ; that is , they are parallel ( I. Def . 6. ) PROPOSITION XIII . THEOREM . A E If two straight lines meeting one another be parallel to two straight lines which meet ...
... fore the planes CD , EF , though produced , do not meet one another ; that is , they are parallel ( I. Def . 6. ) PROPOSITION XIII . THEOREM . A E If two straight lines meeting one another be parallel to two straight lines which meet ...
Side 11
... fore , since LM and LO are at right angles to LG , the com- mon section of the two planes CD and EH , the angle OLM is the inclination of the plane CD to the plane EH ( I. Def . 4 ) . For the same reason the angle MKN is the inclination ...
... fore , since LM and LO are at right angles to LG , the com- mon section of the two planes CD and EH , the angle OLM is the inclination of the plane CD to the plane EH ( I. Def . 4 ) . For the same reason the angle MKN is the inclination ...
Side 12
... fore ABF is a right angle ; but GFB is likewise a right angle ; therefore AB is parallel to FG . And AB is at right angles to the plane CK ; therefore FG is also at right angles to the same plane ( I. 7 ) . But one plane is at right ...
... fore ABF is a right angle ; but GFB is likewise a right angle ; therefore AB is parallel to FG . And AB is at right angles to the plane CK ; therefore FG is also at right angles to the same plane ( I. 7 ) . But one plane is at right ...
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Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ... A. Bell Uten tilgangsbegrensning - 1837 |
Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ... William Chambers,Robert Chambers,A Bell Ingen forhåndsvisning tilgjengelig - 2018 |
Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ... William Chambers,Robert Chambers,A Bell Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
absciss altitude angle ABC assymptotes base centre CG² circumference common section cone Conic Sections conic surface conjugate axis conjugate diameters cord cosine cotangent dicular directrix distance draw EK KF ellipse equal Pl foci focus given angle given point greater Hence hyperbola hypotenuse inclination intercepted intersection Let ABC line be drawn line of common ordinate parabola parallel planes parallelogram pendicular perpen perpendicular perspective plane passing point of contact pole primitive prism projection pyramid ABCD quadrant radius ratio rectangle right angles segments semi-ordinate semicircle sides similar triangles sine small circle solid angle solid KQ solid less solid parallelopipeds sphere spherical angle spherical triangle square straight lines drawn subcontrary surface tangent THEOREM transverse axis vertex vertical wherefore
Populære avsnitt
Side 50 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 15 - DAB : any two of them shall be greater than the third. If the angles BAC, CAD, DAB be all equal, it is evident that any two of them are greater than the third: but if they are not, let BAC be that angle which is not less than either of the other two, and is greater than one of them DAB; and at the point A, in the straight line AB, make, in the plane * 23.
Side 15 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Side 25 - LR, the base of which is the parallelogram LQ, and of which LM is one of its insisting straight lines : therefore, because the parallelogram AB is equal to CD, as the base AB is to the base LQ, so is (7.
Side 16 - EC : (i. ax. 5.) and because DA is equal to AE, and AC common, but the base DC greater than the base EC; therefore the angle DAC is greater than the angle EAC ; (i.
Side 17 - DAB, which contain the solid angle at A, are less than four right angles. Next, let the solid angle at A be contained by any number of plane angles BAC, CAD, DAE, EAF, FAB. These shall together be less than four right angles.
Side 11 - THEOH.—If two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let the straight lines AB, CD be cut by the parallel planes GH, KL, MN, in the points A, E, B; C, F...
Side 11 - FD. Join AC, BD, AD, and let AD meet the plane KL in the point X ; and join EX, XF : because the two parallel planes KL, MN are cut by the plane EBDX, the common sections EX, BD are parallel a.
Side 27 - FC, as the solid HD to the solid DC : But the base HF is equal to the base AE, and the solid GK to the solid AB : therefore, as the base AE to the base CF, so is the solid AB to the solid CD.
Side 1 - The inclination of a straight line to a plane is the acute angle contained by that straight line, and another drawn from the point in which the first line meets the plane, to the point in which...